Hopfion rings in a cubic chiral magnet

Fengshan Zheng (), Nikolai S. Kiselev (), Filipp N. Rybakov (), Luyan Yang, Wen Shi, Stefan Blügel and Rafal E. Dunin-Borkowski
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Fengshan Zheng: South China University of Technology
Nikolai S. Kiselev: Forschungszentrum Jülich
Filipp N. Rybakov: Uppsala University
Luyan Yang: Beijing University of Technology
Wen Shi: Forschungszentrum Jülich
Stefan Blügel: Forschungszentrum Jülich
Rafal E. Dunin-Borkowski: Forschungszentrum Jülich

Nature, 2023, vol. 623, issue 7988, 718-723

Abstract: Abstract Magnetic skyrmions and hopfions are topological solitons1—well-localized field configurations that have gained considerable attention over the past decade owing to their unique particle-like properties, which make them promising objects for spintronic applications. Skyrmions2,3 are two-dimensional solitons resembling vortex-like string structures that can penetrate an entire sample. Hopfions4–9 are three-dimensional solitons confined within a magnetic sample volume and can be considered as closed twisted skyrmion strings that take the shape of a ring in the simplest case. Despite extensive research on magnetic skyrmions, the direct observation of magnetic hopfions is challenging10 and has only been reported in a synthetic material11. Here we present direct observations of hopfions in crystals. In our experiment, we use transmission electron microscopy to observe hopfions forming coupled states with skyrmion strings in B20-type FeGe plates. We provide a protocol for nucleating such hopfion rings, which we verify using Lorentz imaging and electron holography. Our results are highly reproducible and in full agreement with micromagnetic simulations. We provide a unified skyrmion–hopfion homotopy classification and offer insight into the diversity of topological solitons in three-dimensional chiral magnets.

Date: 2023
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DOI: 10.1038/s41586-023-06658-5

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